The Source of Primeness of Rings

Year 2022, Issue: 41, 100 - 104, 31.12.2022

Didem Yeşil , Didem Karalarlıoğlu Camcı

https://doi.org/10.53570/jnt.1189651

Cited By: 1

Abstract

In this study, we define a new concept, i.e., source of primeness of a ring $R$, as $P_{R} := \bigcap_{a\in R} S_{R}^{a}$ such that $S_{R}^{a}:=\{b\in R \mid aRb=(0)\}$. We then examine some basic properties of $P_{R}$ related to the ring’s idempotent elements, nilpotent elements, zero divisor elements, and identity elements. Finally, we discuss the need for further research.

Keywords

Prime ring, semiprime ring, source of primeness, source of semiprimeness

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